Abstract
In this paper, we study the problem of computing the minimum number of searchers who can capture an intruder hiding in a graph. We propose a linear time algorithm for computing the vertex separation and the optimal layout for a unicyclic graph. The best algorithm known so far is given by Ellis et al. (2004) and needs O(n logn) time, where n is the number of vertices in the graph. By a linear-time transformation, we can compute the search number and the optimal search strategy for a unicyclic graph in linear time. We show how to compute the search number for a k-ary cycle-disjoint graph. We also present some results on approximation algorithms.
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Yang, B., Zhang, R., Cao, Y. (2007). Searching Cycle-Disjoint Graphs. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_6
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DOI: https://doi.org/10.1007/978-3-540-73556-4_6
Publisher Name: Springer, Berlin, Heidelberg
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